Properties

 Label 1134.2.l Level $1134$ Weight $2$ Character orbit 1134.l Rep. character $\chi_{1134}(215,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $64$ Newform subspaces $8$ Sturm bound $432$ Trace bound $11$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.l (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$8$$ Sturm bound: $$432$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$5$$, $$11$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1134, [\chi])$$.

Total New Old
Modular forms 480 64 416
Cusp forms 384 64 320
Eisenstein series 96 0 96

Trace form

 $$64 q - 64 q^{4} - 10 q^{7} + O(q^{10})$$ $$64 q - 64 q^{4} - 10 q^{7} - 30 q^{13} + 64 q^{16} - 32 q^{25} + 10 q^{28} + 10 q^{37} + 10 q^{43} - 12 q^{46} + 22 q^{49} + 30 q^{52} - 30 q^{58} - 64 q^{64} - 4 q^{67} + 54 q^{70} - 88 q^{79} + 24 q^{85} - 12 q^{91} - 30 q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(1134, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1134.2.l.a $4$ $9.055$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$-10$$ $$q-\zeta_{12}^{3}q^{2}-q^{4}+(-2\zeta_{12}-2\zeta_{12}^{3})q^{5}+\cdots$$
1134.2.l.b $4$ $9.055$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$-10$$ $$q+\zeta_{12}^{3}q^{2}-q^{4}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots$$
1134.2.l.c $4$ $9.055$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-\zeta_{12}^{3}q^{2}-q^{4}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots$$
1134.2.l.d $4$ $9.055$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\zeta_{12}^{3}q^{2}-q^{4}+(3-2\zeta_{12}^{2})q^{7}+\cdots$$
1134.2.l.e $8$ $9.055$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{24}^{3}q^{2}-q^{4}+(\zeta_{24}^{5}-\zeta_{24}^{6})q^{5}+\cdots$$
1134.2.l.f $8$ $9.055$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{24}^{3}q^{2}-q^{4}+(\zeta_{24}-2\zeta_{24}^{3}+\zeta_{24}^{5}+\cdots)q^{5}+\cdots$$
1134.2.l.g $16$ $9.055$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(\beta _{4}+\beta _{9})q^{2}-q^{4}+(\beta _{1}+\beta _{12}-\beta _{14}+\cdots)q^{5}+\cdots$$
1134.2.l.h $16$ $9.055$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\beta _{4}-\beta _{9})q^{2}-q^{4}+(-\beta _{1}-\beta _{12}+\cdots)q^{5}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(1134, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1134, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(567, [\chi])$$$$^{\oplus 2}$$